Productivity and Economic Growth

Ryoichi Imai


What is GDP?

GDP (gross domestic product) is a sum of values-added created in the country.

Value Added = sales minus costs

In terms of growth rates, we have

GDP growth rate = (GDP this year / GDP last year) minus one.

What is the production function?

In economics, we write the relationship between inputs and outputs as a production function. A typical production function looks like

Output = F ( various Inputs )

In many cases, we aggregate various inputs into capital and labor.

Output = A * F ( capital,   labor )

where * stands for multiplication, and A represents the level of technology or productivity. A production function of this type is called a "Neoclassical Production Function".

What is growth accounting?

We can rewrite this relation in terms of growth rates as follows.

Output growth = Productivity growth + share of capital * Capital growth + share of labor * Labor growth

This equation is called "growth accounting", where the source of economic growth is divided into three factors: capital growth, labor growth, and productivity growth. In general, it is easy to know how large capital growth and labor growth, as well as output growth. Therefore, the equation is used to evaluate how large productivity growth is.

Productivity growth = Output growth - share of capital * capital growth - share of labor * labor growth

The shares of capital and labor has been stable across time and countries. Capital share is approximately 1/3 and labor share is 2/3.

Robert Solow ( a Nobel Prize laureate) found a fact that the GDP growth of the USA was explained by productivity growth to the extent of more than 50 %. 

In most advanced countries, capital and labor no longer grow so fast. Therefore, productivity growth is crucial to long-run economic growth.

What is labor productivity?

Sometimes we discuss productivity growth per capita, which is growth of output per person, and called "labor productivity growth" in newspapers and journals.

labor productivity = output / number of workers employed

Then we can rewrite the neoclassical production function in terms of labor productivity growth.

labor productivity growth = productivity growth + capital share * capital deepening

where capital deepening is growth of capital per person.

Capital per person is a very important concept for economic growth. In countries like USA and Japan, we have a huge amount of capital, which is a result the economic growth and capital accumulation in our past. Then their levels of capital per person are very high. On the contrary, in countries like China or other emerging economies in Asia, Eastern Europe, and Latin America, capital per person is still very low. In most developed countries, capital per person no longer grows so fast, while it grows very fast in countries like China.

Sometimes we are interested in value-added productivity growth, which is contrasted to physical productivity growth.

The value of a product is usually reflected by its price. Even if physical labor productivity (physical output per worker) is growing, it might be the case that its value-added productivity is decreasing.

For example. we have seen a miraculous physical productivity growth in computer industries. However the prices of computers still continue to decline. As a whole, it is doubtful if the value-added productivity of the computer industries are really growing.

On the contrary, even if there is no physical productivity growth, the value-added productivity might grow for some service industries.

For example, in restaurant industries, it is obvious that there is no or very little physical productivity growth. However, some luxurious restaurants are very popular (or sometimes prestigious) not only for its food but also its atmosphere.   

In aggregating individual data, the government statisticians take these price changes into consideration, in order to obtain an appropriate GDP. 

What are the issues?

In Gordon [2001], the professor addresses the following question. To what extent, is the US economic growth in 1990s explained by the IT Revolution?

In Krugman [1999]. the author argues that the growth "miracle" in Asia is not so promising in the future, since the productivity growth rates in those area have been remarkably low.